5 Homogeneous Matrices

The package GradedRingForHomalg defines the classes of graded rings, ring elements and homogeneous matrices over such rings. These three objects can be used as data structures defined in MatricesForHomalg on which the homalg project can rely to do homological computations over graded rings.

The graded rings most prominently can be used with methods known from general homalg rings. The methods for doing the computations are presented in the appendix (B), since they are not for external use. The new attributes and operations are documented here.

Since the objects inplemented here are representations from objects elsewhere in the homalg project (i.e. MatricesForHomalg), we want to stress that there are many other operations in MatricesForHomalg, which can be used in connection with the ones presented here. A few of them can be found in the examples and the appendix of this documentation.

5.1 Homogeneous Matrices: Category and Representations

5.1-1 IsHomalgMatrixOverGradedRingRep

‣ IsHomalgMatrixOverGradedRingRep( A )

( representation )

Returns: true or false

The representation of homalg matrices with entries in a homalg graded ring.